Modelling and feedforward control of wave propagation in an orthotropic rectangular panel based on a transfer matrix method

Abstract

This paper presents a theoretical study on the modelling and active control of bending waves propagating in an orthotropic rectangular panel. The main objectives are to clarify the characteristics of the wave dynamics of an orthotropic rectangular panel and to propose the feedforward control of wave propagation based on a transfer matrix method. As a result of the numerical investigation of the wave dynamics, it is found that there are two types of cut-on frequency in the orthotropic rectangular panel, and the type of bending waves are categorised into progressive, evanescent, and amplitude-varying progressive waves. Next, after the reflected wave absorbing control (RWAC) and the transmitted wave eliminating control (TWEC) laws are derived, numerical simulations on an active wave control system are performed. It is clarified that if the number of control forces is same as that of target mode groups, the RWAC enables the inactivation of vibration modes, and the TWEC enables the vibration-free state in the orthotropic rectangular panel. Moreover, it is concluded that if the number of control forces is lower than that of target mode group, the optimal position of the control force is around the nodal line of the non-targeted mode group which is closer to the disturbance force.